Question

The electric field in a plane electromagnetic wave is given by
$\overrightarrow{E}=200cos\left[\right(0.5\times {10}^3)x-(1.5\times {10}^{11}\left)t\right]\frac{V}{m}\hat{j}$. This wave falls normally on a perfectly reflecting surface having an area of $100{\text{cm}}^2$. If the radiation pressure exerted by the E.M. wave on the surface during a $10$ minute exposure is $\frac{x}{{10}^9}\frac{N}{m^2}$. Find the value of $x$

• A. 353
• B. 353.53
• C. 354

Answer 1

Answer: (A), (B), (C)

Given :-
$\overrightarrow{E}=200cos\left[\right(0.5\times {10}^3)x-(1.5\times {10}^{11}\left)t\right]\frac{V}{m}\hat{j}$
$\Rightarrow E_m=200V/m$

For a perfectly reflecting surface, radiation pressure is :
$P=\frac{2I}{c}$
Also, $I=\frac{(E_m{)}^2}{2{\mu }_{o}c}$

$\Rightarrow P=\frac{(E_m{)}^2}{{\mu }_o{c}^2}$

$P=\frac{{200}^2}{4\pi \times {10}^{-7}\times (3\times {10}^8{)}^2}$

$\Rightarrow P=353.53\times {10}^{-9}N/m^2$

Hence, the value of $x$ is 354.